7.3 Warm-Up

Front

What is a coterminal angle?

Back

Coterminal angles are angles that share the same terminal side when drawn in standard position. To find a coterminal angle, you can add or subtract multiples of 360° (or 2π radians).

Front

How do you find a coterminal angle for -610°?

Back

To find a coterminal angle for -610°, add 360° until the angle is positive: -610° + 720° = 110°. Thus, 110° is coterminal with -610°.

Front

What is the unit circle?

Back

The unit circle is a circle with a radius of 1 centered at the origin (0,0) of the coordinate plane. It is used to define trigonometric functions.

Front

How do you determine the angle in radians from the unit circle coordinates?

Back

To determine the angle in radians from the unit circle coordinates, use the inverse trigonometric functions. For example, if the x-coordinate is -1/2, you can find the angle using the cosine function.

Front

What is the relationship between degrees and radians?

Back

Degrees and radians are two units for measuring angles. To convert degrees to radians, use the formula: radians = degrees × (π/180).

Front

What is the standard position of an angle?

Back

An angle is in standard position when its vertex is at the origin and its initial side lies along the positive x-axis.

Front

How do you graph an angle in standard position?

Back

To graph an angle in standard position, start at the positive x-axis, rotate counterclockwise for positive angles and clockwise for negative angles.

Front

What is exponential decay?

Back

Exponential decay describes a process where a quantity decreases at a rate proportional to its current value, often modeled by the function f(x) = a(1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate.

Front

What is the formula for the value of a depreciating asset?

Back

The formula for the value of a depreciating asset is f(x) = P(1 - r)^x, where P is the initial value, r is the depreciation rate, and x is the number of years.

Front

What is the significance of the x-coordinate in the unit circle?

Back

The x-coordinate in the unit circle represents the cosine of the angle, while the y-coordinate represents the sine of the angle.